If A_1 denotes the area of region bounded by y^2=4 x, x =1 and x -axis in the first quadrant and A_2 denotes the area of region bounded by y^2=4 x, x…

$$\mathrm{A}_{1}=\text { Area }(\text { region } \mathrm{OABO})=\int_{0}^{1} 2 \sqrt{\mathrm{x}} d \mathrm{x}=\left.2\left[\frac{\mathrm{x}^{\frac{3}{2}}}{\dfrac{3}{2}}\right]\right|_{0} ^{1}=\frac{4}{3} $$ $\displaystyle \mathrm{A}_{2}=$ Area $\displaystyle ($ region ODEO $\displaystyle )=2 \int_{0}^{4} 2 \sqrt{\mathrm{x}} d \mathrm{x}=4 \times \frac{2}{3}\left[2^{3}\right]=\frac{64}{3}$ $\displaystyle \mathrm{A}_{1}: \mathrm{A}_{2}=\frac{4}{3}: \frac{64}{3}=1: 16$